An Alternative Choice for the Critical Value of Limits of Agreement and Simulation-Based Sample Size Calculation in Bland Altman Analysis

Bland Altman analysis is a statistical method for assessing the degree of agreement between two methods of measurement. In medical and health sciences, it is a popular method because of its simple calculation and visualization. Under normality assumption, the calculation is based on two sufficient statistics and s, where is the sample mean of differences and s is the sample standard deviation of the differences. The interval is referred to as 95% limits of agreement (LOA) in literature. In a seminar paper, Bland and Altman [2] interpreted LOA as “If the differences are normally distributed, 95% of differences will lie between these limits”. This interpretation seems to be widely accepted, but there is a caveat because the coverage probability of LOA is a random variable. In this article, we demonstrate the sampling distribution of its coverage probability by simulation, and we discuss an alternative choice for the critical value. In addition, using simulation, we perform sample size calculation which satisfies a specified condition for the sampling distribution of coverage probability.